Most, most 1903A3's shoot fine at a 100 with a bottom of the bull hold.
The rear sight slides on the dovetail and is either staked on or has a set screw depending on early or latter production. If your rifle is a virgin then that should be ok there, but if not and it's been messed with then that can cause you problems. There were a lot of people in the past few years that were buying up surplus 03A3 receivers that were former drill rifles. They would cut welds, remove barrels and rebuild those into guns using a lot of Chinese repo parts. Anything goes when it comes to those. Here is the military sight blade number system for the 03A3:
A .537
B .522
C .507
D .492
E .477
As you can see, the A is the tallest. I would measure the A on it and see if it's correct per the list above.
In your case, a piece of steel, .050 thick and about .096 higher would do it given your results with what you have now.
As to barrel pressure;. The military put anywhere from 4-6 pounds of pressure at the last inch of the stock. Competition shooters often put up to 10 pounds of pressure there. Seldom will a 03A3 shoot well with 0 pressure at the tip. If you take the action out of the stock, you will see there is a raised area in the stock at the tip, that's why it's there.
Good luck